Video posted on social media shows it floating away on the river in the northern Indian state of Haryana.
It later got stuck on a bank of tall grass and the man, said to be the son of a local landlord, tried to rescue it.
Police are investigating the incident, local media report.
BMW cars cost around 3.5m rupees (Rs 1 754 700) locally, with Jaguars costing about 4-5m rupees.
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